Such are the four distinct helps, towards facility of syllogizing, enumerated by Aristotle. It will be observed that the third and fourth (study of Resemblances and Differences) bear more upon matters of fact and less upon words; while the second (τὸ ποσαχῶς), though doubtless also bearing on matters of fact and deriving from thence its main real worth, yet takes its departure from terms and propositions, and proceeds by comparing multiplied varieties of these in regard to diversity of meaning. Upon this ground it is, apparently, that Aristotle has given so much fuller development to the second head than to the third and fourth; for, in the Topica, he is dealing with propositions and counter-propositions — with opinions and counter-opinions, not with science and truth.
He proceeds to indicate the different ways in which these three helps (the second, third, and fourth) further the purpose of the dialectician — respondent as well as assailant. Unless the different meanings of the term be discriminated, the respondent cannot know clearly what he admits or what he denies; he may be thinking of something different from what the assailant intends, and the syllogisms constructed may turn upon a term only, not upon any reality.[66] The respondent will be able to protect himself better against being driven into contradiction, if he can distinguish the various meanings of the same term; for he will thus know whether the syllogisms brought against him touch the real matter which he has admitted.[67] On the other hand, the assailant will have much facility in driving his opponent into contradiction, if he (the assailant) can distinguish the different meanings of the term, while the respondent cannot do so; in those cases at least where the proposition is true in one sense of the term and false in another.[68] This manner of proceeding, however, is hardly consistent with genuine Dialectic. No dialectician ought ever to found his interrogations and his arguments upon a mere unanalysed term, unless he can find absolutely nothing else to say in the debate.[69]
[66] Ibid. xviii. p. 108, a. 22.
[67] Ibid. a. 26: χρήσιμον δὲ καὶ πρὸς τὸ μὴ παραλογισθῆναι καὶ πρὸς τὸ παραλογίσασθαι. εἰδότες γὰρ ποσαχῶς λέγεται οὐ μὴ παραλογισθῶμεν, ἀλλ’ εἰδήσομεν ἐὰν μὴ πρὸς τὸ αὐτὸ τὸν λόγον ποιῆται ὁ ἐρωτῶν.
[68] Ibid. a. 29: αὐτοί τε ἐρωτῶντες δυνησόμεθα παραλογίσασθαι ἐὰν μὴ τυγχάνῃ εἰδὼς ὁ ἀποκρινόμενος ποσαχῶς λέγεται· τοῦτο δ’ οὐκ ἐπὶ πάντων δυνατόν, ἀλλ’ ὅταν ᾖ τῶν πολλαχῶς λεγομένων τὰ μὲν ἀληθῆ, τὰ δὲ ψευδῆ.
[69] Topic. I. xviii. p. 108, a. 34: διὸ παντελῶς εὐλαβητέον τοῖς διαλεκτικοῖς τὸ τοιοῦντον, τὸ πρὸς τοὔνομα διαλέγεσθαι, ἐὰν μή τις ἄλλως ἐξαδυνατῇ περὶ τοῦ προκειμένου διαλέγεσθαι.
The third help (an acquaintance with Differences) will be of much avail on all occasions where we have to syllogize upon Same and Different, and where we wish to ascertain the essence or definition of any thing; for we ascertain this by exclusion of what is foreign thereunto, founded on the appropriate differences in each case.[70]
[70] Ibid. b. 2.
Lastly, the fourth help (the intelligent survey of Resemblances) serves us in different ways:— (1) Towards the construction of inductive arguments; (2) Towards syllogizing founded upon assumption; (3) Towards the declaration of definitions. As to the inductive argument, it is founded altogether on a repetition of similar particulars, whereby the universal is obtained.[71] As to the syllogizing from an assumption, the knowledge of resemblances is valuable, because we are entitled to assume, as an Endoxon or a doctrine conformable to common opinion, that what happens in any one of a string of similar cases will happen also in all the rest. We lay down this as the major proposition of a syllogism; and thus, if we can lay hold of any one similar case, we can draw inference from it to the matter actually in debate.[72] Again, as to the declaration of definitions, when we have once discovered what is the same in all particular cases, we shall have ascertained to what genus the subject before us belongs;[73] for that one of the common predicates which is most of the essence, will be the genus. Even where the two matters compared are more disparate than we can rank in the same genus, the knowledge of resemblances will enable us to discover useful analogies, and thus to obtain a definition at least approximative. Thus, as the point is in a line, so is the unit in numbers; each of them is a principium; this, therefore, is a common genus, which will serve as a tolerable definition. Indeed this is the definition of them commonly given by philosophers; who call the unit principium of number, and the point principium of a line, thus putting one and the other into a genus common to both.[74]
[71] Ibid. b. 9.